[R-sig-ME] MCMCglmm: Within- versus between-individual covariances

[Ned Dochtermann]

Jarrod,
Thank you very much for getting back to me so promptly. I am curious about
your suggestion of modelling this within the random component of the model.
Assuming the same data structure as before but adding a fourth trait
measured at the same time as "2" below, would I then add a column
"test.block" with A's for 1&3 and B's for 2&4 and add the MCMCglmm
equivalent of "+ (1|test.block)"? Sorry, I realize this is a pretty basic
question but most of my mixed model experience has been restricted to
fitting random intercepts to individuals along with the occasional intercept
& slope model for individuals.

The whole issue of priors, their implications, and their proper
specification is something I'm still working through. In the priors for R
the covariances for the non-identified parameters were indeed 0 so it seems
like that may be the most straightforward way to deal with it in this case. 

Thanks a lot for your time.
Ned






-----Original Message-----
From: Jarrod Hadfield [mailto:j.hadfield at ed.ac.uk] 
Sent: Sunday, September 05, 2010 9:53 AM
To: Ned Dochtermann
Cc: r-sig-mixed-models at r-project.org
Subject: Re: [R-sig-ME] MCMCglmm: Within- versus between-individual
covariances

Hi Ned,

Currently it is not possible to specify covariance matrices with  
arbitrary covariances set to zero. If you can reorder the terms so  
that the covariance matrix has a block structure (eg swap trait 2 and  
3 in your example) then you can fit this is in the random terms.  
However, the residual term can only be specified by a single term so  
this is not possible. You can still run the model with a us structure  
of course, but as you are aware the posterior distribution for the  
non-identified covariances will simply be the prior distribution.

Cheers,

Jarrod

Quoting Ned Dochtermann <ned.dochtermann at gmail.com>:

> I tried to find an answer to this problem but either failed to select the
> proper search terms or this topic hasn't been discussed. I apologize if
the
> former. I've also consulted the "class notes" for MCMCglmm but that hasn't
> clarified the issue for me.
>
> I am currently working on the analysis of some repeated measures
behavioural
> data and am attempting to estimate variances and covariances among
> behaviours. Specifically we're looking to estimate the between-individual
> (co)variance matrix and I was using a multi-response model and the Poisson
> family in MCMCglmm to do so.
>
> I had thought that the posterior modes for the (co)variance matrix (i.e.
> posterior.modes(model$VCV)) was producing this on the latent scale, with
the
> ".ID" terms being the between individual (co)variances and the ".unit"
terms
> being the within/residual indvidual (co)variances. This conclusion was
based
> on Jarrod Hadfield's appendix to the recent animal model paper published
in
> the Journal of Animal Ecology (2009). In the appendix discussing MCMCglmm
> for repeated measures, repeatability is calculated using the .ID variance
as
> the between individual component and the .unit variance as the within
> individual component.
>
> The problem I've encountered is that due to the experimental design
certain
> aspects of the within individual covariance matrix should not be
> estimatable, but estimates are nonetheless reported. This is, of course,
due
> to my misspecification of the model.
>
> To use an example provided by a colleague, consider a situation where
three
> distinct behaviours are measured and we're interested in their covariance.
> Due to aspects of the experimental manipulation all the behaviours cannot
be
> measured on the same days. Thus the data might look something like:
>
> ID	Day	Behav1	Behav2	Behav3
> 1	1	4		NA		10
> 1	2	3		NA		15
> 1	3	NA		5		NA
> 1	4	NA		4		NA
> 2	1	2		NA		12
> 2	2	1		NA		18
> 2	3	NA		4		NA
> 2	4	NA		3		NA
> ...
> N	1	6		NA		8
> N	2	5		NA		6
> N	3	NA		8		NA
> N	4	NA		7		NA
> [[note, I know these fictitious data aren't necessarily Poisson
distributed
> but the actual data are]]
>
> In this case between individual variances and covariances can be
calculated
> among all three behaviours and within individual covariances should be
> calculated between Behav1 and Behav3 but not for Behav2 with either 1 or 3
> due to separation.
>
> In attempting the initial analyses I specified the random statement using
an
> unstructured matrix:
>> random=~us(trait):ID
> (I'm pretty sure that's what I want and what produces the between
individual
> covariance matrix)
>
> I also kept the residual covariance matrix as the default unstructured:
>> rcov=~us(trait):units
>
> However, if the within-individual/residual covariances really shouldn't be
> calculated between Behav2 and the other two responses, rcov should
actually
> look something like:
>
> v.B1		0		cov.B1*3
> 0		v.B2		0
> cov.B1*3	0		v.B3
>
> For this example "~us" is thus estimating two extra parameters that
> shouldn't be estimated (for the actual dataset these elements have
> credibility intervals overlapping 0).
>
> Clearly idh wouldn't be appropriate for this either but none of the
options
> listed in Table 3.1 of the Class Notes for MCMCglmm seem correct. It also
> doesn't look like I can specify the matrix structure directly (which is
how
> my colleague dealt with this concern using ASreml and which I know SAS
> allows for regular mixed models).
>
> Is there any advice on how best to deal with this issue? I'm at a loss.
>
> Thanks a lot,
> Ned Dochtermann
>
>
> --
> Ned Dochtermann
> Department of Biology
> University of Nevada, Reno
>
> ned.dochtermann at gmail.com
> http://wolfweb.unr.edu/homepage/mpeacock/Dochter/
> --
>
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>
>



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